Pocket Games
Dots and Boxes
Dots and Boxes is the margin-of-the-exercise-book game everyone played at school and almost nobody played well. It has a real strategy, and it comes down to a sentence that sounds absurd: at some point you have to refuse two boxes in order to take ten.
The rules
A grid of dots. Players take turns drawing a segment between two neighbouring dots. Whoever completes the fourth side of a box claims it — and plays again. You continue until the grid is full; whoever has more boxes wins.
On Pocket Games the bot game is played on a 5×5 grid with three difficulty levels; two players on the same phone can choose between 4×4 and 5×5. Against the bot the highest number of boxes closed in a game is saved, per difficulty.
The three phases of a game
Phase 1: the safe moves. At the start almost every line is harmless. A line is safe if it leaves no box with three sides, meaning ready to be given away. You keep going while such moves exist.
Phase 2: who runs out first. At some point every available move opens something. Whoever is forced to move first loses control, and the game is very largely decided here: the number of safe moves available, and who exhausts them first, is what strong players count from the beginning.
Phase 3: the chains. The grid has split into chains, sequences of connected boxes. Whoever opens a chain gives the whole thing to their opponent, who eats it and then has to open the next one. From here the game is already decided, and knowing how it works is everything.
The double cross: the move that wins games
Here is where almost everyone gets it wrong. Your opponent has opened a chain of, say, five boxes. Instinct says: take them all. But if you take them all, you are the one who has to open the next chain, and you hand it over.
The right move is to take only three and leave the last two, closing them with a single line that puts both at your opponent’s disposal. They are forced to take those two boxes, and then it is their turn to open the next chain.
You have given away two boxes and bought control for the rest of the game. With several long chains on the board, this move — the double cross — changes the result by ten or twenty boxes.
When not to do it: if that was the last chain, take everything. The sacrifice exists to pass the turn, and on the final chain there is nothing left to pass.
The parity rule
There is a way to know in advance who will win, and strong players use it to decide their opening moves. In short: count the long chains (three boxes or more) that are forming. You want their number to be even if you moved first, odd if you moved second — because that is how the last chain, the one you take without giving anything back, falls to you.
You do not need to calculate it perfectly: it is enough to notice whether it suits you to create one more long chain or one fewer, and in phase 1 there is still plenty of time to steer it.
Frequently asked questions
If I close a box, do I play again?
Yes, and you keep going as long as you keep closing boxes. An open chain is eaten in a single turn.
Should I always take every box available?
No, and this is the central concept of the game: giving up the last two boxes of a chain forces your opponent to open the next one. On grids with several chains, anyone who does not do it loses.
Does the bot know this strategy?
At the high level yes: when forced to open, it gives away the shortest chain, and it recognises the boxes it can take for free. At the easy level it plays at random.
What size is the grid?
Against the bot, 5×5; two players can also choose 4×4, which is quicker but where parity matters even more.
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